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ws5 - Rob Bayer Instructions Math 55 Worksheet Introduce...

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Rob Bayer Math 55 Worksheet June 29, 2009 Instructions Introduce yourselves! Despite popular belief, math is in fact a team sport! Find some blackboard space, a piece of chalk, and decide who will be your first scribe. Do the problems below, having a different person be the scribe for each one. Try to work out the problems as a group, but feel free to flag me down if you run into a wall. Functions and Sets 1. Determine whether each of the following are injections, surjections, bijections, or none of the three. (a) f : R R ,f ( x ) = 3 x - 2 (b) f : R Z ,f ( x ) = b x c (c) f : N N ,f ( n ) = n + 1 (d) f : R R ,f ( x ) = x ( x - 3)( x + 2) 2. Decide whether each of the following are true or false. For those that are true, prove it. For those that are false, provide a counterexample. (a) If f,g are injective, then f g is (b) If f,g are surjective, then f g is (c) If f g is injective, then f is. (d) If
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